This is about things. All things. Anything you can think.
If Its A Thing Then It Can Be Put Into A Category
Its because if its a thing then it has properties and categories are made on basis of properties.
A thing cannot exist without having any property. A zero property is a nothing (no existence).
Note that the meaning of existence is not limited to physical existence here. Anything that you can imagine is a thing. The only requirement is that it has atleast one property.
If you are imagining it then it already fulfill that requirement because when you are thinking about a thing you are necessarily thinking about its properties.
Categories are made on basis of properties. All things that have certain properties are included. Those things that dont have the certain properties are not included. Categories don't work on exclusion principle. They work on inclusion principle.
The use of the word "properties" (plural) is for brevity. Consider it to include "property" (singular) too. Its distracting and ugly to use "properties/property" or "propert(y/ies)".
A category is a human construct. Out of the hundreds of properties things usually have we consider only a handful. If a thing has all of those properties then its included in the category. If a thing don't have all of those properties then its not included in the category.
We don't have to pay attention to where the things that are not included in any category in consideration go to. A category is an arbitrary thing. We can make any category we want, we just have to decide about what properties to include. Thats it. We include properties and because of this all things that have all of those properties get included in the category. Note that I keep saying "include", I didn't say "exclude" when talking about definition of a category. We humans don't have enough brain cells to put each and everything in universe and in our imagination in a category.
We Make Categories For Purposes. These Purposes Are Operations To Perform.
Categories are means to an end, not end themselves. The end is the operations to perform on the things in the categories.
Categories tells us whats common in things, thats all they do. We want to know whether a thing in consideration has certain properties to find out whether we can perform certain operations on them. If we ignore categorizing things and attempt to apply a function (do an operation) on a thing anyway then we will fail if its a real world thing and get nonsense result if the thing is something in our mind.
Value Of A Property Is Not A Consideration For Including A Thing In a Category. Existence Of The Property Is. Existence Of Value In The Property Is Not.
Value of a property can be anything. It can even be a zero. It don't matter what the value is. As long as there is a property to hold the value the thing is included.
The value may be absent because its currently unknown. Often we have to operate on incomplete data. We cannot expect to always fully know a thing. Thats true even in the limited framework in which we see the thing.
The frameworks we work in are always limited because we work on only a subset of all the properties of a thing. We only work on properties relevant to the operations we want to perform on the things.
So, even though we have already limited ourselves to a subset of properties of things in consideration those properties themselves may be lacking in values. Its not just a may be case actually, its the norm, its common. Almost always we have to work on incomplete data. Ofcourse not all of the operations we want to perform can work on incomplete data. Some operations do require presence of all values. We will look at this in detail in the next section.
I will conclude this section by pointing out a case in which even when all the relevant information is present a field (a property) is not filled yet (don't have a value) just because it has not reached point in time where it get that value, and may be it used to have a value in the field but don't currently have one. For example husband-name is a field in a thing called Sara thats of the category Women. It may happen that Sara currently have no husband, may be she never married or may be she used to have a husband but don't have one at present for any reason. The field husband-name for Sara have to have no value. The value is absent. Its not because we don't have all the relevant information about Sara, we do, its just that our information tell us that the field is empty, its definitely empty. We know for certain that the field currently have no value in it.
Distinguish between "not knowing the value" and "the property don't currently have a value" by using "N/A" for "don't know" and "null" for "don't have".
"null" would mean the property don't currently have a value but it can in future or it had in past or atleast it could have in past.
"N/A" should stand for "not available", not "not applicable". Its because if it has to be "not applicable" then the property itself shouldn't exist.
Operations Are Defined For Range Of Values
There are operations that can only be performed on only some values of a property, not on other values. For example division is an operation that cannot be performed when denominator has value zero.
This is to be distinguished from "not defining an operation for a category". For example, Matrices is a category, division is an operation thats not defined for this category. There is no matrix that can divide.
There are however numbers that can divide. Its just one number zero that cannot divide. The operation Division is defined on all numbers except zero.
So, what happens if you try to apply an operation on a range of values its not defined for? You don't get an answer. You get a confusion.
You get two candidate answers for an operation that can have only one result. Its not like solving a quadratic equation which can have two results. A division is an operation that can have only one result.
Its also unlike trying to apply an operation on a category for which the operation is not defined. You don't get any answer or you get a nonsense answer, but you don't get multiple candidate answers for one vacancy of result.
When you apply a right operation on a wrong range you get more candidate answers than number of vacancies in the result. Thats what confusion means. If you can only pick two but have three candidates all of them valid then you are confused. For confusion the choices not have to be equally important or even nearly equally important, they just have to be all valid which they are if they are candidates.
